Prijs van elektriciteit

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 17 Nov 2010 00:08:56 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh.htm/, Retrieved Wed, 17 Nov 2010 01:07:45 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

23,645 23,755 24,136 24,369 24,713 25,657 26,165 26,366 26,504 26,339 25,897 26,386 26,698 27,701 28,15 28,433 28,96 30,931 31,513 31,569 31,755 30,89 30,381 30,967 31,552 32,097 32,473 32,848 33,1 34,962 35,744 36,496 36,273 34,872 34,919 34,96 36,006 36,086 36,741 36,799 36,438 38,047 38,403 38,471 38,265 37,388 36,655 37,074 37,184 37,306 37,393 37,117 37,424 39,216 39,507 39,592 39,578 38,781 38,325 38,188 38,6 38,832 39,066 39,487 39,539 41,635 42,406 43,35 40,801 39,441 38,935 38,626 38,975 39,107 39,312 39,485 39,468 41,169 41,172 41,497 40,25 39,752 39,754

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 34.9255301204819 0.588381341560461 59.358663597073 Geometric Mean 34.4801687489182 Harmonic Mean 33.9965362097244 Quadratic Mean 35.3295973321322 Winsorized Mean ( 1 / 27 ) 34.9154819277108 0.5861932101987 59.5630951028512 Winsorized Mean ( 2 / 27 ) 34.9060843373494 0.581330809101483 60.045130570838 Winsorized Mean ( 3 / 27 ) 34.9095180722892 0.578745900483376 60.3192489884287 Winsorized Mean ( 4 / 27 ) 34.9104337349398 0.572974572788045 60.9284170588384 Winsorized Mean ( 5 / 27 ) 34.9671204819277 0.561020313153862 62.3277262196704 Winsorized Mean ( 6 / 27 ) 34.9578674698795 0.554030013787359 63.0974254100548 Winsorized Mean ( 7 / 27 ) 34.934 0.543792884420206 64.2413701996979 Winsorized Mean ( 8 / 27 ) 34.9029638554217 0.535012275571304 65.237687898191 Winsorized Mean ( 9 / 27 ) 34.9056746987952 0.534417274630031 65.3153937117019 Winsorized Mean ( 10 / 27 ) 34.8888072289157 0.531842130021581 65.5999313696716 Winsorized Mean ( 11 / 27 ) 34.9025903614458 0.528602408553514 66.02805775508 Winsorized Mean ( 12 / 27 ) 34.925 0.52258486200414 66.8312508442376 Winsorized Mean ( 13 / 27 ) 35.0770843373494 0.492594775105269 71.208803077242 Winsorized Mean ( 14 / 27 ) 35.1494457831325 0.478551693403936 73.4496320201371 Winsorized Mean ( 15 / 27 ) 35.2002289156626 0.469454198289769 74.9811782361256 Winsorized Mean ( 16 / 27 ) 35.2985421686747 0.451456026348611 78.1882179182993 Winsorized Mean ( 17 / 27 ) 35.5840602409639 0.402871993179534 88.3259716321514 Winsorized Mean ( 18 / 27 ) 35.6664698795181 0.382507690018268 93.243798256225 Winsorized Mean ( 19 / 27 ) 35.6538795180723 0.37854090413419 94.1876535103146 Winsorized Mean ( 20 / 27 ) 35.6362891566265 0.374228503100839 95.2260152857037 Winsorized Mean ( 21 / 27 ) 35.7640602409639 0.352366525353439 101.496758822624 Winsorized Mean ( 22 / 27 ) 35.7502771084337 0.348105110820043 102.699661674647 Winsorized Mean ( 23 / 27 ) 35.7439036144578 0.346163079122787 103.257411810169 Winsorized Mean ( 24 / 27 ) 35.7679036144578 0.334942710534397 106.788123728355 Winsorized Mean ( 25 / 27 ) 35.8555542168675 0.318279309955513 112.654367077392 Winsorized Mean ( 26 / 27 ) 35.9247831325301 0.29599535781964 121.369414024460 Winsorized Mean ( 27 / 27 ) 36.0383132530120 0.277829526757335 129.713762513403 Trimmed Mean ( 1 / 27 ) 34.9607901234568 0.577064744242934 60.5838261169857 Trimmed Mean ( 2 / 27 ) 35.0083924050633 0.566379856322659 61.8108006742378 Trimmed Mean ( 3 / 27 ) 35.0635324675325 0.556808545662112 62.9723317659173 Trimmed Mean ( 4 / 27 ) 35.1203466666667 0.546623481427617 64.2496121369372 Trimmed Mean ( 5 / 27 ) 35.1800136986301 0.536550188192539 65.567051270898 Trimmed Mean ( 6 / 27 ) 35.2297887323944 0.528160261604207 66.7028386902665 Trimmed Mean ( 7 / 27 ) 35.2297887323944 0.51986401154178 67.7673159715597 Trimmed Mean ( 8 / 27 ) 35.3462985074627 0.512171166644142 69.0126676576883 Trimmed Mean ( 9 / 27 ) 35.4170615384615 0.504568366030334 70.1927903588239 Trimmed Mean ( 10 / 27 ) 35.4919206349206 0.495247451842895 71.6650242274837 Trimmed Mean ( 11 / 27 ) 35.5739836065574 0.484143527183369 73.478176633938 Trimmed Mean ( 12 / 27 ) 35.6598474576271 0.471004311915622 75.7102356719302 Trimmed Mean ( 13 / 27 ) 35.7490175438597 0.455864749796785 78.4202278412529 Trimmed Mean ( 14 / 27 ) 35.7490175438597 0.44347510415732 80.6111035517743 Trimmed Mean ( 15 / 27 ) 35.9028113207547 0.430796449141124 83.3405460800198 Trimmed Mean ( 16 / 27 ) 35.9790392156863 0.416590906644221 86.3653974243207 Trimmed Mean ( 17 / 27 ) 36.0510816326531 0.402402058304671 89.589704845291 Trimmed Mean ( 18 / 27 ) 36.0995957446808 0.394868384798283 91.4218436685484 Trimmed Mean ( 19 / 27 ) 36.1439777777778 0.388959517886416 92.9247803837842 Trimmed Mean ( 20 / 27 ) 36.1937674418605 0.381489015758247 94.874992324279 Trimmed Mean ( 21 / 27 ) 36.2501951219512 0.371957247772021 97.4579614702643 Trimmed Mean ( 22 / 27 ) 36.2994615384615 0.364068667141612 99.7049864891068 Trimmed Mean ( 23 / 27 ) 36.3554594594595 0.353681032378832 102.791657259467 Trimmed Mean ( 24 / 27 ) 36.4185142857143 0.339199332515368 107.366114242174 Trimmed Mean ( 25 / 27 ) 36.486696969697 0.321558366576339 113.468349022214 Trimmed Mean ( 26 / 27 ) 36.5542903225806 0.301457517446215 121.258513080877 Trimmed Mean ( 27 / 27 ) 36.6235862068966 0.279485591498514 131.039263994013 Median 36.799 Midrange 33.4975 Midmean - Weighted Average at Xnp 36.1244047619048 Midmean - Weighted Average at X(n+1)p 36.1937674418605 Midmean - Empirical Distribution Function 36.1937674418605 Midmean - Empirical Distribution Function - Averaging 36.1937674418605 Midmean - Empirical Distribution Function - Interpolation 36.2501951219512 Midmean - Closest Observation 36.1244047619048 Midmean - True Basic - Statistics Graphics Toolkit 36.1937674418605 Midmean - MS Excel (old versions) 36.1937674418605 Number of observations 83

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh/1uztq1289952532.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh/1uztq1289952532.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh/2uztq1289952532.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t128995246510k113hbpl3o7xh/2uztq1289952532.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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